{
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   "source": [
    "using Plots, Measures, LaTeXStrings, Distributions"
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      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "f1(x) = 3(x-0.4)^2 /x^0.1+2-log(x)/5+3\n",
    "mmm = x_grid[argmin([3(x-0.4)^2 /x^0.1+2-log(x)/5+3 for x in x_grid])]\n",
    "f2(x) = (x-1.2)^2/x^0.15 + 0.8+3\n",
    "x_grid=0:0.01:1\n",
    "\n",
    "p1 = plot(x_grid,f1.(x_grid),label = L\"\\widetilde{E}_{\\textrm{unseen}},~~~\\textrm{Expected~generalization~performance}\", \n",
    "    legend=:outertop, xlabel = \"Model Complexity\", ylabel=\"Error\",lw=2,ticks=false,c=:red)\n",
    "plot!(x_grid,f2.(x_grid),label = L\"\\widetilde{E}_{\\textrm{train}},~~~~~\\textrm{Expected~training~performance}\",lw=2,margin=10mm,c=:green)\n",
    "vspan!([0,0.25],color = :orange, alpha = 0.2,label = \"Under-fitting\")\n",
    "vspan!([0.7,1.0],color = :pink, alpha = 0.2,label = \"Over-fitting\")\n",
    "plot!([mmm,mmm],[3.7,6],c=:black,label=\"Optimal model\",linestyle=:dash)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "savefig(\"../LaTeXBook/figures/chapter_2_figures/performance_error.pdf\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.47"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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